Comparison of analytical techniques for nonlinear vibrations of a parametrically excited cantilever (Q5935705)

The authors study second-order approximations to steady-state principal parametric resonance response of a vertically mounted flexible cantilever beam subjected to a vertical harmonic base motion. The unimodal form of nonlinear equation describing the in-plane large amplitude parametric response of the beam is analyzed using a harmonic balance (HB) method and perturbation method of multiple time scales (MMS). Single-term HB, two-term HB, and second-order MMS with reconstitution version I and version II approximations to the steady-state frequency-amplitude curves of the principal parametric resonance for each of the first four natural modes of the cantilever beam are compared with those obtained by numerical integration of the unimodal equation of motion.